A Positioning Filter based on Uncertainty and Observability Analyses for Nonholonomic Robots

The problem addressed in this paper is the localisation of a mobile robot using a combination of on-board sensors and Ultra-Wideband (UWB) beacons. By using a discretetime formulation of the system’s kinematics, we perform a global observability analysis identifying the geometric conditions that make the system globally observable. Furthermore, the specific algebraic form taken by the system’s evolution allows us to cast the state reconstruction problem into a typical least-squares optimisation framework in order to carry out a thorough uncertainty propagation analysis. The resulting position estimation technique does not require any prior knowledge on the distribution of the noise. Therefore, it compares favourably with Kalman filtering techniques when the knowledge of the noise stochastic features is missing or partial.